Number Sense and Operations

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Number Sense and Operations
Students demonstrate number sense, including an understanding of number systems and operations and how they relate to one another. Students compute fluently and
make reasonable estimates using paper and pencil, technology-supported and mental method.
By the end of the 3-4 program:
  • Use place value structure of the base-ten number system to read, write, represent and compare whole numbers and decimals.

  • Recognize and generate equivalent representations for whole numbers, fractions and decimals.

  • Represent commonly used fractions and mixed numbers using words and physical models.

  • Use models, points of reference and equivalent forms of commonly used fractions to judge the size of fractions and to compare, describe and order them.

  • Recognize and classify numbers as prime or composite and list factors.

  • Count money and make change using coins and paper bills to ten dollars.
By the end of the 5-7 program:

  • Represent and compare numbers less than 0 through familiar applications and extending the number line.

  • Compare, order and convert among fractions, decimals and percents.

  • Develop meaning for percents, including percents greater than 100 and less than 1.

  • Use models and pictures to relate concepts of ratio, proportion and percent.

  • Use order of operations, including use of parenthesis and exponents to solve multi-step problems, and verify and interpret the results.

  • Apply number system properties when performing computations.

By the end of the 8-10 program:
  • Use scientific notation to express large numbers and numbers less than one.

  • Identify subsets of the real number system.

  • Apply properties of operations and the real number system, and justify when they hold for a set of numbers.

  • Connect physical, verbal and symbolic representations of integers, rational numbers and irrational numbers.

  • Compare, order and determine equivalent forms of real numbers.

  • Explain the effects of operations on the magnitude of quantities.

  • Estimate, compute and solve problems involving real numbers, including ratio, proportion and percent, and explain solutions.

Example 3rd grade:
Rewrite 3205 in expanded form
3 x 1000 + 2 x 100 + 5 x 1

Example 6th grade
Solve the following problem by using order of operations
3(9-4)+5-2(10+3)-8=
3(5)+5-2(13)-8=
15+5-26-8=
20-18= 2